You should have entered the competition then. My entry has made it to the front page of FQXi

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I don't see any reason why I should join the competition. The other part is some people around here have a real life (where there are no numbers), I need to work for a daily bread, and to survive day by day in the first place, so I cannot afford time and patience to read all that and than answer.
Cheers.

we can never be sure it's discrete, because then it might be continuous and only our discrete perception is what makes it seem discrete.

and even if we managed to "measure" the emptiness in between the discrete parts, then it could always be a case of aliasing, meaning our discrete perception's resolution isn't high enough for the reality we're trying to observe.

we can never be sure it's discrete, because then it might be continuous and only our discrete perception is what makes it seem discrete.

and even if we managed to "measure" the emptiness in between the discrete parts, then it could always be a case of aliasing, meaning our discrete perception's resolution isn't high enough for the reality we're trying to observe.​

Our perception is better at making discrete action seem to be continuous. Think about movies: If you examine the film, it is a lot of still pictures, yet it looks like continous action.

Classical reality was modelled using continuous functions. With the onset of the digital age and the high expense of early computer memory and limited processing power of early CPU's, the digital approximation was created.

The digital approximation is not exactly full reality, such as a JPEG is not the same as the raw image, but it saves space and can fool the eye into believing it is as good as real. As memory and processing power gets better and cheaper, there may someday be a return to continuous functions.

As an analogy, if go to a ballgame, we will watch it, in reality. The other option is to watch a digital movie of reality. The movie will have distinct frames, with gaps relative to reality. Reality does not contain those gaps. These gaps are there to save memory space and speed up processing.

When the digital movie plays, we may not visually notice the gaps. But if we investigated this movie closer, we would notice that digital creates gaps in reality that we can prove were not in reality. But as long as we don't look too close, we can assume digital is as real as real itself.

If we go all the way down to quantum reality, things exists more like digital since these move in quantum fashion. But as we scale up into macro-reality, macro-reality acts more like the continuous functions of analog.

The orbit of the earth around the sun does not jump and skip space, like a digital movie, but flows in a continuous way. However, all the substructure of its matter will step and jump at the smallest level. The answer would be both.

Various Posts use the following analogy as an argument for a continuous reality.

if we investigated this movie closer, we would notice that digital creates gaps in reality that we can prove were not in reality.​

Actually, the analogy is an argument for a discreet reality.

There is no evidence supporting the notion of continuity at the quantum level. Since the macro level is built on quantum entities & processes, the appearance of continuity is an illusion. Just as the discrete frames of film or video recordings produce the illusion of continuous action to our eyes, the discrete processes at the quantum level produce an illusion of continuous action at the classical level.

We view planetary orbits as continuous because our mind considers a planet to be a solid object which can be modeled by the continuous motion of its center of mass. Actually, a planet is mostly empty space. There is no good reason to believe that there is a center of mass which moves along a continuous path. At the quantum level particles are moving randomly in that mostly empty space.

Calculation of the path of the center of mass would require integrating position/mass variables using a continuous time variable. This would require that the position/motion of each individual quantum particle be describable by continuous functions. Such functions do not exist: The path of quantum level particles cannot be described by continuous functions.

The statistics themselves relate a continuum of probability densities. The particle can always be anywhere within a small continuum. Of course it's hard to trace trajectories for particles jumping in an out of existence. Yet even these show conservation of momentum, a property generally consigned to the continuum of spacetime, at least as far as kinematics is concerned.

Various Posts use the following analogy as an argument for a continuous reality.

if we investigated this movie closer, we would notice that digital creates gaps in reality that we can prove were not in reality.​

Actually, the analogy is an argument for a discreet reality.

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A movie is nothing more than a simulation of real scenes.

There is no evidence supporting the notion of continuity at the quantum level.

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You mean, like wave-particle duality? Or do you mean the uncertainty that a particle can be anywhere within the spacetime continuum plus or minus a very small but continuous range of positions within the band of uncertainty?

Since the macro level is built on quantum entities & processes, the appearance of continuity is an illusion.

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You mean world-scale reality is an illusion because it's just the sum of its parts, that is, Planck length sized domains where particles appear out of thin air, in ambiguous states and virtual in nature, a world of weirdness and paradoxes?

Just as the discrete frames of film or video recordings produce the illusion of continuous action to our eyes, the discrete processes at the quantum level produce an illusion of continuous action at the classical level.

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But reality is nothing like a movie, and a movie is at best only a simulation of something real (or fictional).

We view planetary orbits as continuous because our mind considers a planet to be a solid object

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Except of course for the gas planets, or satellite photos of earth with its clouds, oceans and terrains.

which can be modeled by the continuous motion of its center of mass.

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But reality is not a model. So each particle interacts with every other particle according to real laws that consign their motion to a real trajectory that is not only continuous but relativistic.

Actually, a planet is mostly empty space.

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Quantum or continuum?

There is no good reason to believe that there is a center of mass which moves along a continuous path.

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Which is why you offered it as a mere model.

At the quantum level particles are moving randomly in that mostly empty space.

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And yet they are orbiting the sun predictably.

Calculation of the path of the center of mass would require integrating position/mass variables using a continuous time variable.

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Time and space, you mean. Same for the particles that are orbiting the sun. But you don't have to integrate. You can just sum all the infintesimals - I mean quanta.

This would require that the position/motion of each individual quantum particle be describable by continuous functions.

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Fortunately such a calculation has no practical significance as it would be quite laborious.

Such functions do not exist: The path of quantum level particles cannot be described by continuous functions.

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There are at least two components that determine the particle's position. The first is the result of accounting for its angular acceleration due to gravity during orbit around the sun. That reality manifests as a continuum. The second component is the result of trying to resolve the particle's position so finely, on the order of a Planck length, that the measurement becomes meaningless in relation to the scale of an astronomical unit (times 2π).

BTW, I think the idea of center of mass works well for very large numbers of particles, since the sum of all uncertain quantities x ± Δx over a very large population averages out the uncertainty . . . most of the time.

True if by "reality" you mean the things and processes that exist even if humans do not; however, if you mean a human´s reality, then IMHO it very definitely is a model - one I call the Real Time Simulation created in parietal brain when not in deep sleep:

... {Final link, post 66} gives more details and many supporting facts from many different fields (neurology to historical events) which can best, if not only, be understood from the Real Time Simulation POV...

I just mention three {in this post 21} of the many medical facts supporting this strange POV that "We" are NOT physical bodies (except for periods of deep dreamless sleep) “we” are: "illusion of continuity created by the brain." Or in my own terms, "We" only exist when the Real Time Simulation in parietal brain is executing, creating the world we perceive, our qualia and "us."

(1) After a large parietal stroke, one side of their body is not recognized as being part of the patient / stroke victim. ... Quite commonly when patient is first recovering from their stroke in the hospital bed they will call the nurse, and complain that someone´s leg has been left in the bed. “It is disgusting! - Please remove it”; or in a few cases try to throw their physical leg, which for them is not theirs, out of the bed.

(2) People with "phantom limbs" are the exact opposite case - Their self, constructed in parietal brain, has four normal limbs despite their body having only three. They consciously learn the phantom is not "real" but for them it is real - just as real as their physically existing limbs. ...{behavioral evidence, not just self reports, was here in the original post.}

(3) "Out of body" experiences are caused, usually, by being the reality created in parietal brain. They are not physically real, but are real as it is only by or based on this directly experienced reality by which we INFER the physical world does exist.

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From: http://www.sciforums.com/showpost.php?p=2899438&postcount=21
The RTS is a directly experienced reality, not just one that is inferred to exist - your "physical reality," which may not exist. (Bishop Berkeley argued consistently that it may not exist more than 300 years ago and no one has been able to destroy his POV - his logical arguments.)